<h2>Problem 46</h2>
<div style="color:#666;font-size:80%;">20 June 2003</div><br />
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<p>It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.</p>
<p style='margin-left:10px;'>9 = 7 + 2<img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' />1<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /><br />
15 = 7 + 2<img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' />2<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /><br />
21 = 3 + 2<img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' />3<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /><br />
25 = 7 + 2<img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' />3<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /><br />
27 = 19 + 2<img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' />2<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /><br />
33 = 31 + 2<img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' />1<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /></p>
<p>It turns out that the conjecture was false.</p>
<p>What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?</p>

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